A092824 Farey-factorial numerators.

1, 2, 3, 4, 6, 8, 12, 16, 18, 24, 30, 40, 48, 60, 72, 80, 90, 96, 120, 144, 180, 240, 288, 360, 432, 480, 540, 576, 600, 720, 840, 1008, 1260, 1440, 1680, 2016, 2160, 2520, 2880, 3024, 3360, 3600, 3780, 4032, 4200, 4320, 5040, 5760, 6720, 8064, 10080

Offset: 1

Author

Clark Kimberling, Mar 06 2004

Keywords

• nonn

Comments

The last number in the n-th segment is n!. Let f(n) be the first number in segment n; except for initial terms, f is A001048 and A059171. Let g(n) be the second number in segment n; except for initial terms, g is A052747. Except for the initial terms, the number of numbers in segment n is given by A015614.

Examples

			The sequence begins with these segments:
  1
  2
  3 4 6
  8 12 16 18 24
For the next segment, start with these Farey fractions of order 5:
  1/4 1/3 2/5 1/2 3/5 2/3 3/4 4/5 5/5.
Multiply these by 5! to get
  30 40 48 60 72 80 90 96 120.
		

Crossrefs

Cf. A000142, A001048, A015614, A059171, A052747.

Programs

Mathematica

f[n_] := n! * Table[a/b, {b, 1, n}, {a, 1, b}] // Flatten // Union // Rest; Flatten[Table[f[n], {n, 1, 8}] /. {} -> {1}][[1 ;; 51]] (* Jean-François Alcover, May 18 2011 *)

Formula

Let S(n) be the set of integers an!/b, where a/b ranges through the positive Farey fractions of order n. A092824 is the increasing sequence of integers in the union of the sets S(n), for n>=1.